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The hypothesis of a PeVatron in the Galactic Center, emerged with the recent{\gamma}-ray measurements of H.E.S.S., motivates the search for neutrinos fromthis source. The effect of {\gamma}-ray absorption is studied: at the energiescurrently probed, the known background radiation fields lead to small effects,whereas it is not possible to exclude large effects due to new IR radiationfields near the very Center. Precise upper limits on neutrino fluxes arederived and the underlying hypotheses are discussed. The expected number ofevents for ANTARES, IceCube and KM3NeT, based on the H.E.S.S. measurements, arecalculated. It is shown that km3-class telescopes in the Northern hemispherehave the potential of observing high-energy neutrinos from this importantastronomical object and can check the existence of a hadronic PeV galacticaccelerator.

Neutrinos and {\gamma}-rays from the Galactic Center Region After H.E.S.S. Multi-TeV Measurements